Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31771139 | C2 | semidirect |
| 2. C2×C4×D1076 | C2 | semidirect |
| 3. #31770936 | C2 | semidirect |
| 4. #31770919 | C2 | semidirect |
| 5. #31770906 | C2 | semidirect |
| 6. #31770821 | C2 | semidirect |
| 7. #31770758 | C2 | semidirect |
| 9. #31770718 | C2 | semidirect |
| 10. #31770707 | C2 | semidirect |
| 11. #432×C269 | C2 | semidirect |
| 17. #22575445 | C22 | semidirect |
| 18. #22575441 | C22 | semidirect |
| 22. C4×Dic538 | C22 | semidirect |
| 27. C4×D1076 | C22 | semidirect |
| 32. #22575387 | C22 | semidirect |
| 33. #22575385 | C22 | semidirect |
| 34. #22575378 | C22 | semidirect |
| 37. #22575375 | C22 | semidirect |
| 39. C4⋊C8×C269 | C22 | semidirect |
| 42. #97×C269 | C22 | semidirect |
| 140. C269 | #3114 | semidirect |
| 152. #432 | D269 | semidirect |
| 176. C4⋊C8 | C2×D269 | semidirect |
| 183. #97 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771139 | 2 |
| C2×C4×D1076 | 2 |
| #31770936 | 2 |
| #31770919 | 2 |
| #31770906 | 2 |
| #31770821 | 2 |
| #31770758 | 2 |
| #31770741 | 2 |
| #31770718 | 2 |
| #31770707 | 2 |
| #432×C269 | 2 |
| #3114 | 269 |